Digital Signal Processing Reference
In-Depth Information
System response by convolution for an LTI system
EXAMPLE 10.2
We continue Example 10.1 to illustrate the use of the convolution sum. Let the system input
be given by
x[1] = 3;
x[2] = 4.5;
x[3] = 6;
x[n] = 0, all other n.
The signal
x
[
n
] is shown plotted in Figure 10.4(a). From (10.16), the response
y
[
n
] is given by
y[n] =
q
k=-
q
x[n - k]h[k].
x
[
m
]
6
h
[
k
]
3
1/3
•••
•••
•••
•••
0
1
2
3
4
m
1
0
1
2
3
k
n
n
1
n
2
n
3
n
4
k
n
m
(a)
x
t
[
k
]
x
[
n
k
]
6
4.5
3
•••
•••
n
4
n
3
n
2
n
1
n
k
(b)
h
[
k
]
1/3
•••
•••
4
3
2
1
0
1
2
3
k
6
4.5
x
[0
k
]
3
•••
•••
4
3
2
1
0
1
2
3
k
(c)
Figure 10.4
Signals for Example 10.2.
